Today Databricks announced [0] 6b parameter model from EleutherAI finetuned on Alpaca dataset. According to their CEO[1], training took 3 hours, and costed $30. They didn't release any details on how it was trained, but likely with LoRa.
[0] https://www.databricks.com/blog/2023/03/24/hello-dolly-democ... [1] https://twitter.com/alighodsi/status/1639251347777388544